In reality, there was no 5th Armored Infantry unit as part of the 29th Infantry in WW2's European theater of operations. The 29th was made up of the 115th, 116th, and 175th Infantry Regiments, the 110th, 111th, 224th, and 227th Field Artillery Battalions, and the 121st Engineer Combat Battalion. It isn't clear if the military units were arranged differently in the universe of Star Trek, or if the discrepancy was in reality a shortcoming of the holoprogram's accuracy.